Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.8%

Time: 10.8s

Alternatives: 12

Speedup: 1.2×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (z * -6.0)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * (4.0d0 + (z * (-6.0d0))))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (z * -6.0)));
}

Python

def code(x, y, z):
	return x + ((y - x) * (4.0 + (z * -6.0)))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(4.0 + Float64(z * -6.0))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (4.0 + (z * -6.0)));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

   11. distribute-lft-neg-out N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

   16. metadata-eval 99.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))))
   (if (<= z -0.5)
     t_0
     (if (<= z -3.2e-297) (* x -3.0) (if (<= z 0.65) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -3.2e-297) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * 6.0d0)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-3.2d-297)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -3.2e-297) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -3.2e-297:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -3.2e-297)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -3.2e-297)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -3.2e-297], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.650000000000000022 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)}\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(-6 \cdot \left(y - x\right) + 4 \cdot \frac{y - x}{z}\right) + \color{blue}{\frac{x}{z}}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{x}{z} + \color{blue}{\left(-6 \cdot \left(y - x\right) + 4 \cdot \frac{y - x}{z}\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(-6 \cdot \left(y - x\right) + 4 \cdot \frac{y - x}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\color{blue}{-6 \cdot \left(y - x\right)} + 4 \cdot \frac{y - x}{z}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \color{blue}{4} \cdot \frac{y - x}{z}\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \frac{4 \cdot \left(y - x\right)}{\color{blue}{z}}\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \frac{\left(y - x\right) \cdot 4}{z}\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \left(y - x\right) \cdot \color{blue}{\frac{4}{z}}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \left(y - x\right) \cdot \frac{4 \cdot 1}{z}\right)\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \left(y - x\right) \cdot \left(4 \cdot \color{blue}{\frac{1}{z}}\right)\right)\right)\right) \]

      12. distribute-lft-out N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \color{blue}{\left(-6 + 4 \cdot \frac{1}{z}\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \left(4 \cdot \frac{1}{z} + \color{blue}{-6}\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \left(4 \cdot \frac{1}{z} + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \left(4 \cdot \frac{1}{z} - \color{blue}{6}\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(4 \cdot \frac{1}{z} - 6\right)}\right)\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{4 \cdot \frac{1}{z}} - 6\right)\right)\right)\right) \]

      18. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(4 \cdot \frac{1}{z} + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(4 \cdot \frac{1}{z} + -6\right)\right)\right)\right) \]

      20. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(-6 + \color{blue}{4 \cdot \frac{1}{z}}\right)\right)\right)\right) \]

      21. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(-6, \color{blue}{\left(4 \cdot \frac{1}{z}\right)}\right)\right)\right)\right) \]

      22. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(-6, \left(\frac{4 \cdot 1}{\color{blue}{z}}\right)\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(-6, \left(\frac{4}{z}\right)\right)\right)\right)\right) \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{z} + \left(y - x\right) \cdot \left(-6 + \frac{4}{z}\right)\right)} \]

   6. Taylor expanded in x around -inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(x \cdot \left(3 \cdot \frac{1}{z} - 6\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(x \cdot \left(3 \cdot \frac{1}{z} - 6\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(3 \cdot \frac{1}{z} - 6\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(3 \cdot \frac{1}{z} - 6\right)\right)\right)}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\left(3 \cdot \frac{1}{z} - 6\right)}\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(3 \cdot \frac{1}{z} - 6\right)}\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \left(3 \cdot \frac{1}{z} + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \left(3 \cdot \frac{1}{z} + -6\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \left(-6 + \color{blue}{3 \cdot \frac{1}{z}}\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \color{blue}{\left(3 \cdot \frac{1}{z}\right)}\right)\right)\right)\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \left(\frac{3 \cdot 1}{\color{blue}{z}}\right)\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \left(\frac{3}{z}\right)\right)\right)\right)\right) \]

      12. /-lowering-/.f64 56.4%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 56.4%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(0 - \left(-6 + \frac{3}{z}\right)\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot x\right)}\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{6}\right)\right) \]

       2. *-lowering-*.f64 56.3%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{6}\right)\right) \]

   11. Simplified 56.3%

       \[\leadsto z \cdot \color{blue}{\left(x \cdot 6\right)} \]

   if -0.5 < z < -3.19999999999999972e-297

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 96.1%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 65.1%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 65.1%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -3.19999999999999972e-297 < z < 0.650000000000000022

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 60.7%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 60.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 58.5%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 58.5%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot 6\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-297}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z 6.0))))
   (if (<= z -0.5)
     t_0
     (if (<= z -4.2e-297) (* x -3.0) (if (<= z 0.52) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -4.2e-297) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * 6.0d0)
    if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-4.2d-297)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * 6.0);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -4.2e-297) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * 6.0)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -4.2e-297:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * 6.0))
	tmp = 0.0
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -4.2e-297)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * 6.0);
	tmp = 0.0;
	if (z <= -0.5)
		tmp = t_0;
	elseif (z <= -4.2e-297)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -4.2e-297], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.52000000000000002 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-6 \cdot \left(y - x\right) + \left(4 \cdot \frac{y - x}{z} + \frac{x}{z}\right)\right)}\right) \]

      2. associate-+r+ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\left(-6 \cdot \left(y - x\right) + 4 \cdot \frac{y - x}{z}\right) + \color{blue}{\frac{x}{z}}\right)\right) \]

      3. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{x}{z} + \color{blue}{\left(-6 \cdot \left(y - x\right) + 4 \cdot \frac{y - x}{z}\right)}\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\left(\frac{x}{z}\right), \color{blue}{\left(-6 \cdot \left(y - x\right) + 4 \cdot \frac{y - x}{z}\right)}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\color{blue}{-6 \cdot \left(y - x\right)} + 4 \cdot \frac{y - x}{z}\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \color{blue}{4} \cdot \frac{y - x}{z}\right)\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \frac{4 \cdot \left(y - x\right)}{\color{blue}{z}}\right)\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \frac{\left(y - x\right) \cdot 4}{z}\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \left(y - x\right) \cdot \color{blue}{\frac{4}{z}}\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \left(y - x\right) \cdot \frac{4 \cdot 1}{z}\right)\right)\right) \]

      11. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot -6 + \left(y - x\right) \cdot \left(4 \cdot \color{blue}{\frac{1}{z}}\right)\right)\right)\right) \]

      12. distribute-lft-out N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \color{blue}{\left(-6 + 4 \cdot \frac{1}{z}\right)}\right)\right)\right) \]

      13. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \left(4 \cdot \frac{1}{z} + \color{blue}{-6}\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \left(4 \cdot \frac{1}{z} + \left(\mathsf{neg}\left(6\right)\right)\right)\right)\right)\right) \]

      15. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \left(\left(y - x\right) \cdot \left(4 \cdot \frac{1}{z} - \color{blue}{6}\right)\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(4 \cdot \frac{1}{z} - 6\right)}\right)\right)\right) \]

      17. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{4 \cdot \frac{1}{z}} - 6\right)\right)\right)\right) \]

      18. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(4 \cdot \frac{1}{z} + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(4 \cdot \frac{1}{z} + -6\right)\right)\right)\right) \]

      20. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(-6 + \color{blue}{4 \cdot \frac{1}{z}}\right)\right)\right)\right) \]

      21. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(-6, \color{blue}{\left(4 \cdot \frac{1}{z}\right)}\right)\right)\right)\right) \]

      22. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(-6, \left(\frac{4 \cdot 1}{\color{blue}{z}}\right)\right)\right)\right)\right) \]

      23. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(-6, \left(\frac{4}{z}\right)\right)\right)\right)\right) \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{z} + \left(y - x\right) \cdot \left(-6 + \frac{4}{z}\right)\right)} \]

   6. Taylor expanded in x around -inf

      \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(x \cdot \left(3 \cdot \frac{1}{z} - 6\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(x \cdot \left(3 \cdot \frac{1}{z} - 6\right)\right)\right)\right) \]

      2. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(3 \cdot \frac{1}{z} - 6\right)\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(\left(3 \cdot \frac{1}{z} - 6\right)\right)\right)}\right)\right) \]

      4. neg-sub0 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \left(0 - \color{blue}{\left(3 \cdot \frac{1}{z} - 6\right)}\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \color{blue}{\left(3 \cdot \frac{1}{z} - 6\right)}\right)\right)\right) \]

      6. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \left(3 \cdot \frac{1}{z} + \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \left(3 \cdot \frac{1}{z} + -6\right)\right)\right)\right) \]

      8. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \left(-6 + \color{blue}{3 \cdot \frac{1}{z}}\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \color{blue}{\left(3 \cdot \frac{1}{z}\right)}\right)\right)\right)\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \left(\frac{3 \cdot 1}{\color{blue}{z}}\right)\right)\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \left(\frac{3}{z}\right)\right)\right)\right)\right) \]

      12. /-lowering-/.f64 56.4%

          \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(0, \mathsf{+.f64}\left(-6, \mathsf{/.f64}\left(3, \color{blue}{z}\right)\right)\right)\right)\right) \]

   8. Simplified 56.4%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(0 - \left(-6 + \frac{3}{z}\right)\right)\right)} \]

   9. Taylor expanded in z around inf

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

          \[\leadsto \left(-1 \cdot -6\right) \cdot \left(\color{blue}{x} \cdot z\right) \]

       2. associate-*r* N/A

          \[\leadsto -1 \cdot \color{blue}{\left(-6 \cdot \left(x \cdot z\right)\right)} \]

       3. associate-*l* N/A

          \[\leadsto -1 \cdot \left(\left(-6 \cdot x\right) \cdot \color{blue}{z}\right) \]

       4. *-commutative N/A

          \[\leadsto -1 \cdot \left(z \cdot \color{blue}{\left(-6 \cdot x\right)}\right) \]

       5. associate-*r* N/A

          \[\leadsto \left(-1 \cdot z\right) \cdot \color{blue}{\left(-6 \cdot x\right)} \]

       6. associate-*r* N/A

          \[\leadsto \left(\left(-1 \cdot z\right) \cdot -6\right) \cdot \color{blue}{x} \]

       7. *-commutative N/A

          \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot z\right) \cdot -6\right)} \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\left(-1 \cdot z\right) \cdot -6\right)}\right) \]

       9. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(z \cdot -1\right) \cdot -6\right)\right) \]

       10. associate-*l* N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{\left(-1 \cdot -6\right)}\right)\right) \]

       11. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot 6\right)\right) \]

       12. *-lowering-*.f64 56.2%

           \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{6}\right)\right) \]

   11. Simplified 56.2%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot 6\right)} \]

   if -0.5 < z < -4.20000000000000027e-297

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 96.1%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 65.1%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 65.1%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -4.20000000000000027e-297 < z < 0.52000000000000002

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 60.7%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 60.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 58.5%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 58.5%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.58) t_0 (if (<= z 0.64) (+ (* y 4.0) (* x -3.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.64) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-0.58d0)) then
        tmp = t_0
    else if (z <= 0.64d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.64) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -0.58:
		tmp = t_0
	elif z <= 0.64:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.64)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.64)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.58], t$95$0, If[LessEqual[z, 0.64], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.640000000000000013 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(y - x\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot -6\right) \cdot \left(\color{blue}{y} - x\right) \]

      3. associate-*r* N/A

         \[\leadsto z \cdot \color{blue}{\left(-6 \cdot \left(y - x\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-6 \cdot \left(y - x\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-6, \color{blue}{\left(y - x\right)}\right)\right) \]

      6. --lowering--.f64 99.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-6, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   if -0.57999999999999996 < z < 0.640000000000000013

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{\frac{2}{3} \cdot \frac{2}{3} - z \cdot z}{\color{blue}{\frac{2}{3} + z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(y - x\right) \cdot 6\right) \cdot \frac{1}{\color{blue}{\frac{\frac{2}{3} + z}{\frac{2}{3} \cdot \frac{2}{3} - z \cdot z}}}\right)\right) \]

      3. un-div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - x\right) \cdot 6}{\color{blue}{\frac{\frac{2}{3} + z}{\frac{2}{3} \cdot \frac{2}{3} - z \cdot z}}}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\left(y - x\right) \cdot 6\right), \color{blue}{\left(\frac{\frac{2}{3} + z}{\frac{2}{3} \cdot \frac{2}{3} - z \cdot z}\right)}\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\left(y - x\right), 6\right), \left(\frac{\color{blue}{\frac{2}{3} + z}}{\frac{2}{3} \cdot \frac{2}{3} - z \cdot z}\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), 6\right), \left(\frac{\color{blue}{\frac{2}{3}} + z}{\frac{2}{3} \cdot \frac{2}{3} - z \cdot z}\right)\right)\right) \]

      7. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), 6\right), \left(\frac{1}{\color{blue}{\frac{\frac{2}{3} \cdot \frac{2}{3} - z \cdot z}{\frac{2}{3} + z}}}\right)\right)\right) \]

      8. flip-- N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), 6\right), \left(\frac{1}{\frac{2}{3} - \color{blue}{z}}\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), 6\right), \mathsf{/.f64}\left(1, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), 6\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{2}{3}\right), \color{blue}{z}\right)\right)\right)\right) \]

      11. metadata-eval 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), 6\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\frac{2}{3}, z\right)\right)\right)\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot 6}{\frac{1}{0.6666666666666666 - z}}} \]

   5. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + 4 \cdot \left(y - x\right)} \]
   6. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto 4 \cdot \left(y - x\right) + \color{blue}{x} \]

      2. sub-neg N/A

         \[\leadsto 4 \cdot \left(y + \left(\mathsf{neg}\left(x\right)\right)\right) + x \]

      3. mul-1-neg N/A

         \[\leadsto 4 \cdot \left(y + -1 \cdot x\right) + x \]

      4. distribute-rgt-in N/A

         \[\leadsto \left(y \cdot 4 + \left(-1 \cdot x\right) \cdot 4\right) + x \]

      5. *-commutative N/A

         \[\leadsto \left(4 \cdot y + \left(-1 \cdot x\right) \cdot 4\right) + x \]

      6. mul-1-neg N/A

         \[\leadsto \left(4 \cdot y + \left(\mathsf{neg}\left(x\right)\right) \cdot 4\right) + x \]

      7. distribute-lft-neg-in N/A

         \[\leadsto \left(4 \cdot y + \left(\mathsf{neg}\left(x \cdot 4\right)\right)\right) + x \]

      8. *-commutative N/A

         \[\leadsto \left(4 \cdot y + \left(\mathsf{neg}\left(4 \cdot x\right)\right)\right) + x \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \left(4 \cdot y + \left(\mathsf{neg}\left(4\right)\right) \cdot x\right) + x \]

      10. metadata-eval N/A

          \[\leadsto \left(4 \cdot y + -4 \cdot x\right) + x \]

      11. associate-+r+ N/A

          \[\leadsto 4 \cdot y + \color{blue}{\left(-4 \cdot x + x\right)} \]

      12. +-commutative N/A

          \[\leadsto 4 \cdot y + \left(x + \color{blue}{-4 \cdot x}\right) \]

      13. distribute-rgt1-in N/A

          \[\leadsto 4 \cdot y + \left(-4 + 1\right) \cdot \color{blue}{x} \]

      14. metadata-eval N/A

          \[\leadsto 4 \cdot y + -3 \cdot x \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\left(4 \cdot y\right), \color{blue}{\left(-3 \cdot x\right)}\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(y \cdot 4\right), \left(\color{blue}{-3} \cdot x\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(\color{blue}{-3} \cdot x\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \left(x \cdot \color{blue}{-3}\right)\right) \]

      19. *-lowering-*.f64 95.8%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(y, 4\right), \mathsf{*.f64}\left(x, \color{blue}{-3}\right)\right) \]

   7. Simplified 95.8%

      \[\leadsto \color{blue}{y \cdot 4 + x \cdot -3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* (- y x) -6.0))))
   (if (<= z -0.58) t_0 (if (<= z 0.5) (+ x (* (- y x) 4.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * ((y - x) * (-6.0d0))
    if (z <= (-0.58d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * ((y - x) * -6.0);
	double tmp;
	if (z <= -0.58) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * ((y - x) * -6.0)
	tmp = 0
	if z <= -0.58:
		tmp = t_0
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(Float64(y - x) * -6.0))
	tmp = 0.0
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * ((y - x) * -6.0);
	tmp = 0.0;
	if (z <= -0.58)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.58], t$95$0, If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

         \[\leadsto \left(-6 \cdot z\right) \cdot \color{blue}{\left(y - x\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(z \cdot -6\right) \cdot \left(\color{blue}{y} - x\right) \]

      3. associate-*r* N/A

         \[\leadsto z \cdot \color{blue}{\left(-6 \cdot \left(y - x\right)\right)} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(-6 \cdot \left(y - x\right)\right)}\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-6, \color{blue}{\left(y - x\right)}\right)\right) \]

      6. --lowering--.f64 99.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(-6, \mathsf{\_.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 95.8%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))))
   (if (<= y -6.5e+51) t_0 (if (<= y 2.1e+58) (* x (+ -3.0 (* z 6.0))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -6.5e+51) {
		tmp = t_0;
	} else if (y <= 2.1e+58) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    if (y <= (-6.5d+51)) then
        tmp = t_0
    else if (y <= 2.1d+58) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -6.5e+51) {
		tmp = t_0;
	} else if (y <= 2.1e+58) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	tmp = 0
	if y <= -6.5e+51:
		tmp = t_0
	elif y <= 2.1e+58:
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -6.5e+51)
		tmp = t_0;
	elseif (y <= 2.1e+58)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (y <= -6.5e+51)
		tmp = t_0;
	elseif (y <= 2.1e+58)
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+51], t$95$0, If[LessEqual[y, 2.1e+58], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e51 or 2.10000000000000012e58 < y

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(-6 \cdot \frac{x \cdot \left(\frac{2}{3} - z\right)}{y} + \left(6 \cdot \left(\frac{2}{3} - z\right) + \frac{x}{y}\right)\right)} \]

   5. Simplified 91.8%

      \[\leadsto \color{blue}{y \cdot \left(\left(4 + z \cdot -6\right) + \frac{x \cdot \left(6 \cdot z + -3\right)}{y}\right)} \]

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(4 + -6 \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(4, \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{-6}\right)\right)\right) \]

      3. *-lowering-*.f64 84.1%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{-6}\right)\right)\right) \]

   8. Simplified 84.1%

      \[\leadsto y \cdot \color{blue}{\left(4 + z \cdot -6\right)} \]

   if -6.5e51 < y < 2.10000000000000012e58

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{1}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right) + 1\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + -1 \cdot z\right) + 1\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(-1 \cdot z + \frac{2}{3}\right) + 1\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(-1 \cdot z\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(z \cdot -1\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -4\right) + 1\right)\right) \]

      10. associate-+l+ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + -3\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \left(1 + \color{blue}{-4}\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-6 \cdot z\right) \cdot -1\right), \color{blue}{\left(1 + -4\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(-6 \cdot z\right)\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-1 \cdot -6\right) \cdot z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(6 \cdot z\right), \left(1 + -4\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      18. metadata-eval 75.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 75.1%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+51}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z)))))
   (if (<= y -6.4e+51) t_0 (if (<= y 2.2e+59) (* x (+ -3.0 (* z 6.0))) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -6.4e+51) {
		tmp = t_0;
	} else if (y <= 2.2e+59) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    if (y <= (-6.4d+51)) then
        tmp = t_0
    else if (y <= 2.2d+59) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -6.4e+51) {
		tmp = t_0;
	} else if (y <= 2.2e+59) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	tmp = 0
	if y <= -6.4e+51:
		tmp = t_0
	elif y <= 2.2e+59:
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	tmp = 0.0
	if (y <= -6.4e+51)
		tmp = t_0;
	elseif (y <= 2.2e+59)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	tmp = 0.0;
	if (y <= -6.4e+51)
		tmp = t_0;
	elseif (y <= 2.2e+59)
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+51], t$95$0, If[LessEqual[y, 2.2e+59], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4000000000000005e51 or 2.2e59 < y

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 83.9%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 83.9%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -6.4000000000000005e51 < y < 2.2e59

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + -6 \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} - z\right) + \color{blue}{1}\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right)\right) + 1\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(\frac{2}{3} + -1 \cdot z\right) + 1\right)\right) \]

      5. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(-6 \cdot \left(-1 \cdot z + \frac{2}{3}\right) + 1\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(-1 \cdot z\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot \left(z \cdot -1\right) + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      8. associate-*l* N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -6 \cdot \frac{2}{3}\right) + 1\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\left(\left(-6 \cdot z\right) \cdot -1 + -4\right) + 1\right)\right) \]

      10. associate-+l+ N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \color{blue}{\left(-4 + 1\right)}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + -3\right)\right) \]

      12. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \left(\left(-6 \cdot z\right) \cdot -1 + \left(1 + \color{blue}{-4}\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-6 \cdot z\right) \cdot -1\right), \color{blue}{\left(1 + -4\right)}\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(-1 \cdot \left(-6 \cdot z\right)\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      15. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(\left(-1 \cdot -6\right) \cdot z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\left(6 \cdot z\right), \left(1 + -4\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), \left(\color{blue}{1} + -4\right)\right)\right) \]

      18. metadata-eval 75.1%

          \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(\mathsf{*.f64}\left(6, z\right), -3\right)\right) \]

   5. Simplified 75.1%

      \[\leadsto \color{blue}{x \cdot \left(6 \cdot z + -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+51}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+145}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-36}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.6e+145)
   (* x -3.0)
   (if (<= x 1.06e-36) (* 6.0 (* y (- 0.6666666666666666 z))) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e+145) {
		tmp = x * -3.0;
	} else if (x <= 1.06e-36) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.6d+145)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.06d-36) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.6e+145) {
		tmp = x * -3.0;
	} else if (x <= 1.06e-36) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.6e+145:
		tmp = x * -3.0
	elif x <= 1.06e-36:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.6e+145)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.06e-36)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.6e+145)
		tmp = x * -3.0;
	elseif (x <= 1.06e-36)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.6e+145], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.06e-36], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.60000000000000003e145 or 1.05999999999999999e-36 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 56.5%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 51.3%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 51.3%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -2.60000000000000003e145 < x < 1.05999999999999999e-36

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 70.0%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 70.0%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 36.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+136}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-41}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6e+136) (* x -3.0) (if (<= x 5.5e-41) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e+136) {
		tmp = x * -3.0;
	} else if (x <= 5.5e-41) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6d+136)) then
        tmp = x * (-3.0d0)
    else if (x <= 5.5d-41) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6e+136) {
		tmp = x * -3.0;
	} else if (x <= 5.5e-41) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6e+136:
		tmp = x * -3.0
	elif x <= 5.5e-41:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6e+136)
		tmp = Float64(x * -3.0);
	elseif (x <= 5.5e-41)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6e+136)
		tmp = x * -3.0;
	elseif (x <= 5.5e-41)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6e+136], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 5.5e-41], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999958e136 or 5.50000000000000022e-41 < x

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. associate-*l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

      5. sub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

      11. distribute-lft-neg-out N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

      12. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

      14. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

      16. metadata-eval 99.8%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 54.0%

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto x \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 49.1%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

   10. Simplified 49.1%

       \[\leadsto \color{blue}{x \cdot -3} \]

   if -5.99999999999999958e136 < x < 5.50000000000000022e-41

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(\frac{2}{3} - z\right)\right)} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \color{blue}{\left(y \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{2}{3} - z\right)}\right)\right) \]

      3. --lowering--.f64 71.5%

         \[\leadsto \mathsf{*.f64}\left(6, \mathsf{*.f64}\left(y, \mathsf{\_.f64}\left(\frac{2}{3}, \color{blue}{z}\right)\right)\right) \]

   5. Simplified 71.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{4 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{4} \]

      2. *-lowering-*.f64 43.2%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{4}\right) \]

   8. Simplified 43.2%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6 \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) (- 0.6666666666666666 z)) 6.0)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * (0.6666666666666666d0 - z)) * 6.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
}

Python

def code(x, y, z):
	return x + (((y - x) * (0.6666666666666666 - z)) * 6.0)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(0.6666666666666666 - z)) * 6.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * (0.6666666666666666 - z)) * 6.0);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\frac{2}{3} - z\right) \cdot \color{blue}{\left(\left(y - x\right) \cdot 6\right)}\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\left(\frac{2}{3} - z\right) \cdot \left(y - x\right)\right) \cdot \color{blue}{6}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\left(\frac{2}{3} - z\right) \cdot \left(y - x\right)\right), \color{blue}{6}\right)\right) \]

   4. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\left(\frac{2}{3} - z\right), \left(y - x\right)\right), 6\right)\right) \]

   5. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3}\right), z\right), \left(y - x\right)\right), 6\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{2}{3}, z\right), \left(y - x\right)\right), 6\right)\right) \]

   7. --lowering--.f64 99.5%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\frac{2}{3}, z\right), \mathsf{\_.f64}\left(y, x\right)\right), 6\right)\right) \]

4. Applied egg-rr 99.5%

   \[\leadsto x + \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(y - x\right)\right) \cdot 6} \]

5. Final simplification 99.5%

   \[\leadsto x + \left(\left(y - x\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot 6 \]
6. Add Preprocessing

Alternative 11: 25.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

   11. distribute-lft-neg-out N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

   16. metadata-eval 99.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
6. Step-by-step derivation

7. Simplified 54.1%

   \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

8. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto x \cdot \color{blue}{-3} \]

   2. *-lowering-*.f64 29.3%

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{-3}\right) \]

10. Simplified 29.3%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 12: 2.7% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\right)}\right) \]

   2. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - x\right) \cdot \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y - x\right), \color{blue}{\left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(\color{blue}{6} \cdot \left(\frac{2}{3} - z\right)\right)\right)\right) \]

   5. sub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \left(\frac{2}{3} + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \color{blue}{6 \cdot \left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \left(6 \cdot \frac{2}{3} + \left(\mathsf{neg}\left(z\right)\right) \cdot \color{blue}{6}\right)\right)\right) \]

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \color{blue}{\left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)}\right)\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(\left(6 \cdot \frac{2}{3}\right), \left(\left(\mathsf{neg}\left(z\right)\right) \cdot 6\right)\right)\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\color{blue}{\left(\mathsf{neg}\left(z\right)\right)} \cdot 6\right)\right)\right)\right) \]

   11. distribute-lft-neg-out N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(\mathsf{neg}\left(z \cdot 6\right)\right)\right)\right)\right) \]

   12. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(6\right)\right)}\right)\right)\right)\right) \]

   13. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot -6\right)\right)\right)\right) \]

   14. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \left(z \cdot \left(6 \cdot \color{blue}{-1}\right)\right)\right)\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, \color{blue}{\left(6 \cdot -1\right)}\right)\right)\right)\right) \]

   16. metadata-eval 99.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \mathsf{+.f64}\left(4, \mathsf{*.f64}\left(z, -6\right)\right)\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(y, x\right), \color{blue}{4}\right)\right) \]
6. Step-by-step derivation

7. Simplified 54.1%

   \[\leadsto x + \left(y - x\right) \cdot \color{blue}{4} \]

8. Taylor expanded in y around inf

   \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{y}, 4\right)\right) \]
9. Step-by-step derivation

10. Simplified 26.4%

    \[\leadsto x + \color{blue}{y} \cdot 4 \]

11. Taylor expanded in x around inf

    \[\leadsto \color{blue}{x} \]
12. Step-by-step derivation

13. Simplified 2.5%

    \[\leadsto \color{blue}{x} \]
14. Add Preprocessing

Reproduce

herbie shell --seed 2024140 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))